public static int Main(string[] args)
{
if (args.Length != 2)
{
return(1);
}
// The two input parameters will be the name of the file with the table values
// and the amount of lines in that file
string filein = args[0];
int nlines = int.Parse(args[1]);
StreamReader streamin = new StreamReader(filein);
double[] xs = new double[nlines];
double[] ys = new double[nlines];
for (int i = 0; i < nlines; i++)
{
string line = streamin.ReadLine();
// There is a third value in each line (the integral from x[0] to z), but we
// do not need the value here
string[] numbers = line.Split('\t');
xs[i] = double.Parse(numbers[0]);
ys[i] = double.Parse(numbers[1]);
}
streamin.Close();
// Interpolate the data
double xstart = xs[0];
double xend = xs[nlines - 1];
double deltax = 0.02;
var cspline = new cubicspline(xs, ys);
for (double k = xstart; k < xend; k += deltax)
{
double interpval = cspline.eval(k);
double integralval = cspline.integrate(k);
double derivval = cspline.deriv(k);
WriteLine("{0,8:f4}\t{1,8:f4}\t{2,8:f4}\t{3,8:f4}", k, interpval, integralval, derivval);
}
return(0);
}
static void Main()
{
// Accuracy is for the root finding algorithm
double accuracy = 1e-5;
double rmax = 8;
// Auxiliary function that we want to find roots for
Func <vector, vector> M = delegate(vector e){
// e is the energy
// Solve the Schrödinger equation for hydrogen and find the function value
// at the maximum radius.
double frmax = hydrogen.solve(e[0], rmax);
return(new vector(frmax));
};
// The energy should be close to -1/2, so we start somewhere around that area
var rand = new Random();
vector start = new vector(-1 - 0.2 * rand.NextDouble());
// Find the root for the auxiliary function
vector root = roots.newton(M, start, accuracy);
double energy = root[0];
StreamWriter WriteRoot = new StreamWriter("outRootText.txt");
WriteRoot.WriteLine("Trying to find a root for the auxiliary function, M:");
WriteRoot.WriteLine("The analytic root is at energy: \t -1/2.");
WriteRoot.WriteLine("Starting the search from energy: \t {0}.", start[0]);
WriteRoot.WriteLine("A root has been found at energy: \t {0}", energy);
WriteRoot.WriteLine("The deviation from the analytic root is: {0}", -0.5 - energy);
WriteRoot.WriteLine("Convergence criterium: ||M(root)|| < {0}", accuracy);
WriteRoot.Close();
// For simplicity we just solve the ODE again with the found energy to retrieve
// the solution. Thus we avoid passing lots of lists back and forth, most of them
// will just be constantly overwritten anyway until the end.
// Create some lists to save the path of the found solution
List <double> rs = new List <double>();
List <vector> fs = new List <vector>();
// Starting conditions and parameters
double r0 = 1e-4;
vector f0 = new vector(r0 - r0 * r0, 1 - 2 * r0);
double acc = 1e-3;
double eps = 0;
double h = 1e-3;
ode.rk45(hydrogen.diffeq(energy), r0, f0, rmax, h, acc, eps, xlist: rs, ylist: fs);
// Inspired by Rasmus Berg Jensen, let's spline the data points to get a nice curve.
// This is a good strategy if the equations are expensive to solve, since you only
// have few data points then - in the present case it is just easy, practical, and
// serves as a good way to practice the curriculum.
vector rPoints = new vector(rs.Count);
vector fPoints = new vector(fs.Count);
for (int i = 0; i < rs.Count; i++)
{
rPoints[i] = rs[i];
fPoints[i] = fs[i][0];
}
var cspline = new cubicspline(rPoints, fPoints);
double rStart = rPoints[0];
double rEnd = rPoints[rPoints.size - 1];
// Print the data
for (double r = rStart; r < rEnd; r += 0.02)
{
WriteLine("{0,16:f15} \t {1,16:f15}", r, cspline.eval(r));
}
Write("\n\n");
// Print out the analytic solution
for (double r = rStart; r < rEnd; r += 0.02)
{
WriteLine("{0,16:f15} \t {1,16:f15}", r, r * Exp(-r));
}
} // end Main
static void Main(string[] args)
{
// Accuracy is for the root finding algorithm
double accuracy = 1e-5;
double rmax = 8;
bool printAnalytic = false;
bool precise = false;
// Allow the rmax value to be adjusted via input from the terminal
if (args.Length > 0)
{
rmax = double.Parse(args[0]);
}
// If specified, switch the boolean to make the program write out the analytic
// solution also.
if (args.Length > 1)
{
if (args[1] == "print")
{
printAnalytic = true;
}
}
/*
* If specified, use the more precise asymptotic requirement at rmax.
* It is not necessary to be able to specify this at the same time as print
* (analytic solution), since print only has to be done once.
*/
if (args.Length > 1)
{
if (args[1] == "precise")
{
precise = true;
}
}
// Auxiliary function that we want to find roots for
Func <vector, vector> M = delegate(vector e){
// e is the energy
// Solve the Schrödinger equation for hydrogen and find the function value
// at the maximum radius.
double frmax = hydrogen.solve(e[0], rmax);
if (precise)
{
double k = Sqrt(-2 * e[0]);
frmax = frmax - rmax * Exp(-k * rmax);
}
return(new vector(frmax));
};
// The energy should be close to -1/2, so we start somewhere around that area
var rand = new Random();
vector start = new vector(-1 - 0.2 * rand.NextDouble());
// Find the root for the auxiliary function
vector root = roots.newton(M, start, accuracy);
double energy = root[0];
StreamWriter WriteRoot = new StreamWriter("outRootTextLog.txt", true);
WriteRoot.WriteLine("Log entry for root finding for the rmax = {0}, print = {1}" +
", precise = {2} inputs to the Main function.", rmax, printAnalytic, precise);
WriteRoot.WriteLine("Trying to find a root for the auxiliary function, M:");
WriteRoot.WriteLine("Starting the search from energy: \t {0}.", start[0]);
WriteRoot.WriteLine("Used rmax: \t\t\t\t {0}", rmax);
WriteRoot.WriteLine("The analytic root is at energy: \t -1/2.");
WriteRoot.WriteLine("A root has been found at energy: \t {0}", energy);
WriteRoot.WriteLine("The deviation from the analytic root is: {0}", -0.5 - energy);
WriteRoot.WriteLine("Convergence criterium: ||M(root)|| < {0}\n\n", accuracy);
WriteRoot.Close();
// Write out the found root for a plot also, along with the used rmax
if (precise)
{
StreamWriter WriteRootDataP = new StreamWriter("outRootDataP.txt", true);
WriteRootDataP.WriteLine("{0}\t{1}", rmax, energy);
WriteRootDataP.Close();
}
else
{
StreamWriter WriteRootData = new StreamWriter("outRootData.txt", true);
WriteRootData.WriteLine("{0}\t{1}", rmax, energy);
WriteRootData.Close();
}
// For simplicity we just solve the ODE again with the found energy to retrieve
// the solution. Thus we avoid passing lots of lists back and forth, most of them
// will just be constantly overwritten anyway until the end.
// Create some lists to save the path of the found solution
List <double> rs = new List <double>();
List <vector> fs = new List <vector>();
// Starting conditions and parameters
double r0 = 1e-4;
vector f0 = new vector(r0 - r0 * r0, 1 - 2 * r0);
double acc = 1e-3;
double eps = 0;
double h = 1e-3;
ode.rk45(hydrogen.diffeq(energy), r0, f0, rmax, h, acc, eps, xlist: rs, ylist: fs);
// Inspired by Rasmus Berg Jensen, let's spline the data points to get a nice curve.
// This is a good strategy if the equations are expensive to solve, since you only
// have few data points then - in the present case it is just easy, practical, and
// serves as a good way to practice the curriculum.
vector rPoints = new vector(rs.Count);
vector fPoints = new vector(fs.Count);
for (int i = 0; i < rs.Count; i++)
{
rPoints[i] = rs[i];
fPoints[i] = fs[i][0];
}
var cspline = new cubicspline(rPoints, fPoints);
double rStart = rPoints[0];
double rEnd = rPoints[rPoints.size - 1];
// Print the data
if (precise)
{
StreamWriter writeDataP = new StreamWriter("outP.txt", true);
for (double r = rStart; r < rEnd; r += 0.02)
{
writeDataP.WriteLine("{0,16:f15} \t {1,16:f15}", r, cspline.eval(r));
}
// Do the last point outside the loop to avoid precision erros since
// we loop over doubles
writeDataP.WriteLine("{0,16:f15} \t {1,16:f15}", rEnd, cspline.eval(rEnd));
writeDataP.Write("\n\n");
writeDataP.Close();
}
else
{
StreamWriter writeData = new StreamWriter("out.txt", true);
for (double r = rStart; r < rEnd; r += 0.02)
{
writeData.WriteLine("{0,16:f15} \t {1,16:f15}", r, cspline.eval(r));
}
writeData.WriteLine("{0,16:f15} \t {1,16:f15}", rEnd, cspline.eval(rEnd));
writeData.Write("\n\n");
writeData.Close();
}
if (printAnalytic)
{
// Print out the analytic solution from r=0 to r=12.
StreamWriter printAnalyticSol = new StreamWriter("outAnalytic.txt");
for (double r = 0; r < 12; r += 0.02)
{
printAnalyticSol.WriteLine("{0,16:f15} \t {1,16:f15}", r, r * Exp(-r));
}
printAnalyticSol.Close();
}
} // end Main